Is it because I registered the team in an Eternal League (without doing a single match against AI)?

The Cabalvision Official League does not accept outside teams, only teams that were created specifically within, and stayed within, that league. The open ladder and champion ladders are both competitions within that league... the eternal league you moved your team to was not... so it no longer qualifies to play in any COL ladders.

That seems a bit harsh as I didn't even play a single match in Eternal.

I don't think it has any sort of special accounting system to ensure that outside teams played all their games inside a given environment, it just knows if a team is from inside the league, or not inside the league at the time you try to join. Since it wasn't inside the league at the time, it's considered an outside team. Computers are very absolute things.. they're not so big on judgment calls and special considerations.

One more rule that's nowhere to be seen in-game and certainly not intuitive.

It's not really that strange. There was a bit of a kerfuffle half a year ago over the idea of allowing outside teams into COL (CCL was always going to be new teams only). Originally they were going to let them in, but some streamers threw such a tantrum about the idea that they locked COL to inside teams only, always. So... we get what we get, I guess.

In general it works like this: once you're out, you're out... there's no "grace period" to come back in.

It's not really that strange. There was a bit of a kerfuffle half a year ago over the idea of allowing outside teams into COL (CCL was always going to be new teams only). Originally they were going to let them in, but some streamers threw such a tantrum about the idea that they locked COL to inside teams only, always. So... we get what we get, I guess.
In general it works like this: once you're out, you're out... there's no "grace period" to come back in.

Yeah, it's a pain. I took a favored team of mine from CCL at the end of the season and put it in COL so I could still play it. Then when the COL season ended I accidentally quit the league instead of the competition, and now the team can't join any COL seasons even though it hasn't played any other matches outside COL...